1 Answer
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Note: This answer is old (May, 2013), and may be out of date due to changes to the Steam platform. Some users have reported this solution not working. Proceed with caution!

Unfortunately, there is no native feature allowing this, but it is possible. (as of 2013/Jan/25) It will take some work, but you can delete from the Steam cloud by following these instructions:

HOW TO DELETE FILES STORED IN STEAM CLOUD SERVERS

Context:

I've read many times on this forum topics with concerns about
the fact that it's impossible to manage files stored in Steam Cloud
servers. This can be very annoying if you want to know exactly what
files are in the Cloud or to solve sync problems such as savegame
overwriting. Since no good solution was available, I've decided to
look at the issue and try to understand how Steam Cloud works.

Presentation of Steam Cloud:

Steam Cloud is used to backup config
files and savegames online in order to access them from every
computer. It's a feature that can be enabled/disabled through two
different dialogs:

Steam > Settings > Downloads + Cloud > Enable Steam Cloud synchronization for games which support it (will affect all the games)

How it works:

The first thing you should know is that there are most
of the time three versions of your save files:

the original version stored in the game folder or in AppData (S1)

the cloud version stored in Steam\userdata\SteamID\AppID (S2)

the cloud version stored in Steam servers (S3)

When you start a game for the first time, S1 is created. When you close it, S1 is copied to S2 which is then synced to S3.

When you start a game from another computer, if Steam has S3 on its servers but doesn't find S2 on your computer, it will copy S3 to S2. Steam Cloud automatically downloads the missing files each time you start Steam.

You understand that the most important save location for us is S2. If we play a bit with it, we should be able to reach our goal. So what's in S2? Note: some games don't have S1 and write directly to S2, while others don't use the S2 remote folder to store the save files. In this case, the remotecache.vdf file in S2 points directly to the files located in S1 (thanks TheOdds for the detail).

Userdata contents:

In Steam\userdata you should have 1 (or more) folder corresponding to your account ID (SteamID). Open it and you'll find a folder for each game using Steam Cloud you have installed. The folder name is the AppID of the game (found in the URL when you visit its store page, it's a number like 220 for Half-Life 2). In the game folder you'll find:

a remote folder: it contains all the files that are being synced up with Steam servers

a remotecache.vdf file: the file describe the properties (such as file size or modification date) of the files contained in the remote folder

In this tutorial there are 2 main steps:

Bringing up the Cloud Sync
Conflict dialog

Deleting the Cloud files

Note that you have to repeat these steps for EVERY game you want to delete Steam Cloud files!

But first I would like you to delete your AppID folder and restart
Steam: you'll see that it will automatically recreate the AppID folder
and download the missing files from Steam Cloud. This verification is
important for you to make sure that the whole operation has been
successful.

After this long but necessary introduction, let the magic begin!

I. Bringing up the Cloud Sync Conflict dialog

The first part is probably the most difficult. In order to get rid of
the files stored in Steam servers, we'll need the help of the Cloud
Sync Conflict dialog. It appears when the Cloud files differ from the
local files stored on your computer. There are several ways to get it,
I'll give you two:

Exit Steam and make sure that Steam Cloud is enabled.

Alter the content of all files in Steam\userdata\SteamID\AppID\remote. The
objective is that every file becomes different from the ones stored in
the Cloud. You can't simply delete the files otherwise Steam will
download them from the Cloud. You can corrupt them by deleting all
their content. 0 bytes files will indeed do the trick. To do this
(thanks Kevin92 for the tip):

Enable Steam Cloud
and "Sync conflict" should appear in your game status. Note that this
method may not affect all the files (and you need to modify all of
them if you want to delete all of them later).

Once you have "Sync conflict", start your game and the Cloud Sync
Conflict dialog should appear.

II. Deleting the Cloud files

Ok now it's piece of cake. Once the dialog is opened, don't click on
any option.

Go to Steam\userdata\SteamID\AppID and delete ALL the
files in it, remote folder and remotecache.vdf.

Go back to the
Cloud Sync Conflict dialog and click on "Upload to the Steam Cloud".
Steam will sync your AppID folder with nothing in it... meaning that
all the files on the Cloud will be deleted! You don't believe me? Wait
for it, the demonstration is right after

Then the game should start
automatically. But... it will create new files that will be synced
when I'll leave the game!! Indeed it will, except if you...

Alt-tab
the game and disable Steam Cloud.

Return to the game and exit it
(or kill it through process manager). No files will be synced up!

Exit Steam.

Delete the AppID folder.

Note: if you haven't modified all the files in step I, only the
modified ones will be deleted. The others will remain in Steam Cloud.

How to make sure it worked?

Remember at the beginning when I told you to delete your AppID folder
to see that Steam Cloud automatically download the missing files each
time you start Steam? Normally, if there is no file left in Steam
Cloud, it won't download anything on your computer. So here is how to
check it:

Enable Steam Cloud.

Exit Steam.

Delete the AppID
folder (if you didn't do it in step II).

now check S3 (Cloud files) and compare them with S2 (local files).
Nothing in S3? Nothing copied to S2!

Check your
Steam\userdata\SteamID folder. No new AppID folder has been created!

You can eventually check on another computer and see that no files are
downloaded anymore from Steam Cloud.

Congratulations, you have successfully deleted your files from Steam
Cloud.

I know you asked for a quick way to do it, and probably already found this answer if you did any Googling, but I figured I would repost it here for future users since this appears to be the only answer as of 2013/Jan/25.

This excellent guide is from user Homme Crabe on the Steam forums; full credit to the author! I am merely copying here so there is a second copy just in case the original is lost/its URL is altered (plus, we can now edit it).

@aslum Yeah, me too. Hopefully Valve will implement user controlled create, read, update, and delete functionality to the Steam Cloud. I'm sure they have a long list of other things to do first, though.
– Lemmings19Jan 25 '13 at 21:08

Ok this method is great im seeing a lot of people have progress with it but when trying to execute the clc command in powershell both as administrator and as a normal user i get the access denied red line error Are there any fixes for that? I tried making the file not read only and it did nothing it stays read only but im sure thats not the issue this is my laptop i have have all admin privelages and have disabled UAC
– user47941May 3 '13 at 17:05

@Lukman Furthermore, make sure that the file isn't currently in use. The game which uses it should not be running, or perhaps Steam shouldn't be running either. If the file is in use, that will typically lock it from external deletion/modification.
– Lemmings19May 5 '13 at 6:32

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